There is no such thing as immutable, statelessness or whatever.
Parts of your setup may be stateless deployments with immutable images. That is, because you collected all state and put it into one or two selected locations.
You can redeploy everything but these selected locations.
If you drop them, if you make a config mistake, these things are gone gone. They cannot be redeployed, unless you have taken measures to do so. See 1.